Question

You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 1717 years. You expect that the​ drug's profits will be $ 4$4 million in its first year and that this amount will grow at a rate of 5 %5% per year for the next 1717 years. Once the patent​ expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is nbsp 7 % 7% per​ year?

Answer 1

In this given case, the amount of annuity of $4 Million is growing at the rate of 5% over the next 17 years. The present value of the growing annuity is calculated by using the following formula

The Present value of growing annuity = [Annuity / (r – g)] x [1 – {(1+g) / (1 + r)}ⁿ]

Where, Discount Rate (r) = 7%

Growth Rate (g) = 5%

Number of years (n) = 17 Years

Therefore, the The Present value of growing annuity = [Annuity / (r – g)] x [1 – {(1+g) / (1 + r)}ⁿ]

= [$40,00,000 / (0.07 – 0.05)] x [1 – {(1 + 0.05) / (1+ 0.07)}¹⁷]

= [$40,00,000 / 0.02] x [1 – (0.981308)¹⁷]

= [$40,00,000 / 0.02] x [1 – 0.725594]

= $20,00,00,000 x 0.2744057

= $5,48,81,139.62

= $54.881 Million (Converted the dollar amount to Million with 3 decimal place)

“Hence, The present value of the new drug = $5,48,81,139.62 or $54.881 Million”